This is starting to sound like a variation of Helios Flight 522:
Helios Airways Flight 522 - Wikipedia, the free encyclopedia
The left turn may have been an attempt by one of the remaining crew-members to return to land. Some news reports claim it was a low as 3'000 after turning west - other reports say is was sill up near 30k. If it did drop from the cruse this is further evidence that possibly one remaining member of the crew was making a valiant attempt to save the lives of aboard.